The pixels of a natural digital image are highly correlated, namely that there exists a redundancy between image pixels. The objective of image coding is to remove the redundancy so that, with little distortion, much fewer bits can be used to represent an image than simply quantizing individual pixels, such as through PCM. One way to remove redundancy is predictive coding, in which the residual signal between the current pixel and its predicted value is coded. Because the difference value represented by the residual signal contains less redundancy than the pixel itself, coding the difference value is more efficient than coding the pixel itself. The research on predictive coding is summarized by Gersho and Gray in Vector Quantization and Signal Compression, Kluwer Academic Publishers, 1992, herein incorporated by reference.
Transform coding is another way to achieve the objective of redundancy removal. In transform coding, an orthogonal transform is applied to a block of image pixels so that the transform domain coefficients become less correlated than the image domain pixels. The performance of a transform is measured by its decorrelation property and associated energy compaction capability.
Vector quantization (VQ) is a more direct way to take advantage of the pixel correlation characteristics for image coding. Theoretically, VQ is the best quantization technique and its optimality is achieved when the number of vector dimensions approaches infinity. A detailed discussion on the complexity and storage limitations of VQ can be found in Gersho and Gray, supra. Due to the rapid increase in complexity with the number of vector dimensions, in practice, an image is always divided into small blocks and VQ is applied to each block. Then the issue is how to remove redundancy between the blocks. Predictive VQ and finite state VQ have been studied to achieve such inter-vector redundancy removal.
Recently, vector transformation (VT) has been proposed for image coding to remove inter-vector correlation [See W. Li, "Vector Transform Coding, IEEE Trans. Circuits and Systems for Video Technology, Vol. 1, No. 4, 12/91, herein incorporated by reference]. Vector transform coding (VTC) is a vector generalization of the conventional transform coding techniques, which will be referred to as scalar transform coding (STC) in this context. In such a vector generalization, a pixel is replaced by a block of pixels (a vector), the ST which decorrelates scalar pixels is replaced by a VT which decorrelates vectors, and scalar quantization (SQ) in the ST domain is replaced by VQ in the VT domain. It was found in W. Li and Y.-Q. Zhang, "New Insights and Results on Transform Domain VQ of Images," IEEE ICASSP'93, April 1993, and W. Li and Y.-Q. Zhang, "A Study on the Optimal Attributes of Transform Domain Vector Quantization for Image and Video Compression," IEEE ICC'93, May 1993 (herein incorporated by reference) that VR also preserves the intra-vector correlation while decorrelates the inter-vectors, which allows significant performance gain over ST when VQ is used.